Vinv

Matrix of genotype markers (size n x L)

Pre-computation for LxL linear system solve

Tau over sigma from precomputation

tau_over_sigma

Variance component from model noise epsilon

sigma

Matrix or vector on right-hand side of V inverse

This function applies V inverse via the Woodbury matrix identity

The explosion of biobank data offers immediate opportunities for
gene-environment (GxE) interaction studies of complex diseases because of the
large sample sizes and rich collection in genetic and non-genetic information.
However, the extremely large sample size also introduces new computational
challenges in GxE assessment, especially for set-based GxE variance component (VC)
tests, a widely used strategy to boost overall GxE signals and to evaluate the
joint GxE effect of multiple variants from a biologically meaningful unit
(e.g., gene).
We present 'SEAGLE', a Scalable Exact AlGorithm for Large-scale Set-based
GxE tests, to permit GxE VC test scalable to biobank data. 'SEAGLE' employs modern
matrix computations to achieve the same <e2><80><9c>exact<e2><80><9d> results as the original GxE VC
tests, and does not impose additional assumptions nor relies on approximations.
'SEAGLE' can easily accommodate sample sizes in the order of 10^5, is implementable
on standard laptops, and does not require specialized equipment.
The accompanying manuscript for this package can be found at Chi, Ipsen, Hsiao,
Lin, Wang, Lee, Lu, and Tzeng. (2021+) <arXiv:2105.03228>.

Vinv: Function for applying V inverse in Algorithm 1

Description

Usage

Arguments

Value